Pure 3 Overview

Pure Mathematics 3 is the A2 pure paper. It assumes everything in P1 and adds nine topics; the syllabus lists them as algebra, logarithms and exponentials, trigonometry, differentiation, integration, numerical solution of equations, vectors, differential equations and complex numbers. Use this page as a map, and follow the "needs" links on each note to find the P1 ideas it builds on.

Algebra

• Modulus equations and inequalities
• Polynomial division and the factor theorem
• The remainder theorem
• Partial fractions
• Binomial expansion for rational powers

Logarithms and exponentials

• Logarithms and equations with the unknown in the index
• The number $e$ and $\ln x$
• Exponential graphs
• Modelling with logarithmic plots

Trigonometry

• Trigonometry toolkit: every identity and how to choose
• Secant, cosecant and cotangent
• Compound angles
• Double angles
• The $R$-method

Differentiation

• Differentiation in P3: the map
• Product rule and quotient rule
• Differentiating $\ln x$ and $e^x$
• Differentiating trigonometric functions
• Differentiating $\tan^{-1} x$
• Implicit differentiation
• Parametric equations

Integration

• Standard integrals and trigonometric identities
• Integrating $f'(x)/f(x)$ and related forms
• Integration by substitution
• Integration by parts
• Integrating with partial fractions

Differential equations, numerical methods, vectors

• Differential equations
• Numerical solution of equations
• Vectors, vector equation of a line, scalar product

Complex numbers

• Complex numbers: the map, which links all ten notes from the definition of $i$ to loci in the Argand diagram.